Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include<cstdio>
using namespace std;
int a[200100],p[200100];
bool pd(int x1,int x2,int x3){
	int y,z;
	if(x1<x2&&x1<x3) y=x2,z=x3;
	else if(x2<x1&&x2<x3) y=x3,z=x1;
	else if(x3<x1&&x3<x2) y=x1,z=x2;
	if(y<z) return 0;
	return 1;
}
int main(){
//	freopen("F.in","r",stdin);
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&a[i]);
		p[a[i]]=i;
	}
	int T=0,f;
	for(int i=n-1;i>=1;i--)
	{
		if(T==0){
			if(p[i]<p[i+1])
				continue;
			T=1;
			f=i+1;
		}
		else{
			if(pd(p[f],p[i],p[i+1]))
				T++,f=i+1;
		}
	}
	printf("%d\n",T);
	return 0;
}